The invention will be described in the environment of a recursive filter in a video signal processing system, however, it is to be understood that it is not limited to such applications.
In video systems recursive filters may be used to reduce noise in the frequency band of the video signal. From frame-to-frame there is a relatively high degree of signal correlation. Thus, if a video signal from successive frames is summed, the correlated video signal will add linearly, but random noise accompanying the signal will not. The summed signal is generally normalized to a desired amplitude range and the signal-to-noise ratio of the averaged signal is enhanced by the processing.
A typical video recursive filter includes a delay device coupled in a recirculating loop with circuitry for combining a fraction of delayed signal with a fraction of incoming signal. The combined signal is applied to the delay device which delays the combined signal by the time period necessary to insure that constituent parts of each combined video signal samples are from corresponding pixels of successive video frames. The fractional parts of the incoming and delayed signals are obtained by scaling the two signals by factors K and (1-K) respectively. If the amplitude of the incoming signal is equal to the amplitude of the averaged signal from the delay device, the new combined signal will be normalized to equal the input signal. In a digital processing system, the normalization tends to minimize the sample bit size required of the delay device. Thus, if the incoming signal consists of 8-bit samples, the sample size in the delay device can be held to e.g. 9 or 10 bits. This is an important design aspect in reducing the manufacturing costs of recursive filters for consumer applications.
Scaling circuits for use in recursive filters in e.g. consumer television receivers are required to be of relatively simple construction to be cost competitive. One of the simplest scaling circuits and, thus, one which is desirable for use in a digital television receiver, is a bit-shifter. The bit-shifter, or barrel shifter, shifts the bits of a sample rightward to less significant bit positions to perform division and shifts sample bits leftward to more significant bit positions to perform multiplication. In the divide mode, which mode is appropriate to effect scaling by factors less than one, after the sample bits are right shifted, the shifted sample is truncated by discarding a number of least significant bits equal in number to the number of significant bit positions the sample bits were shifted. Truncation without e.g. rounding and truncation with improper rounding will tend to generate significant anomalies in the processed signal. See B. Gold and C. M. Rader, Digital Processing Of Signals, McGraw Hill, 1969, pp. 98-131. In the context of a video signal processing system the truncation/rounding effects of a recursive filter may be manifested as the "ground glass" effect. This is the result of samples applied to the recursive filter having insufficient resolution to permit the filter to converge to the proper values.
Scaling by bit-shifting and truncation is illustrated in Table I.
TABLE I ______________________________________ Right Binary Shift Binary Desired Input Decimal 3 Bit Truncated Decimal Decimal Value Equiv. Pos. Value Equiv. Equiv. ______________________________________ 111.000 7 000.111 000 0 1 110.000 6 000.110 000 0 l 101.000 5 000.101 000 0 1 100.000 4 000.100 000 0 1 011.000 3 000.011 000 0 0 010.000 2 000.010 000 0 0 001.000 1 000.001 000 0 0 000.000 0 000.000 000 0 0 ______________________________________
For illustrative purposes a three bit binary input signal is utilized. All possible three bit binary input values are listed in the leftmost column labelled Binary Input Value and their decimal equivalents are listed in the second column labelled Decimal Equiv. The three-bit input values are written with a decimal point and three trailing zeroes for the pupose of indicating the significance of the bit positions. The third column labelled Right Shift 3 Bit Pos., lists binary values corresponding to the values in the first column which have been right shifted three significant bit positions, i.e. the column one values divided by 8. Typically a scaling circuit will truncate or drop off the trailing bits and the resulting binary values are listed under the column labelled Binary Truncated Value and their corresponding decimal equivalents are shown to the right thereof under the column labelled Decimal Equiv. It is seen that all the right shifted and truncated values have a decimal value of zero. The rightmost column labelled Desired Decimal Equiv. indicates the values that would be produced if the truncated values were properly rounded. The values in this column are determined by assuming that all values having dropped bits, which are equal to or greater than one-half the least significant bit of the truncated value, should have the least significant bit of the truncated value raised by one unit.
J. K. Moore in U.S. Pat. No. 4,195,350 entitled "Method And Apparatus For Eliminating Deadband In Digital Recursive Filters" discloses a method and apparatus for reducing the effects of truncating scaled samples in a recursive filter. In this system samples are scaled by bit shifting. Then the absolute value of the scaled sample is truncated by dropping a number of least significant digits determined by the value of the scale factor. If any of the dropped bits is a logic "one" value, the value of the truncated sample is incremented by one unit. The incremented, truncated sample is then complemented or not depending on whether the scaled sample was negative or positive respectively.
U.S Pat. No. 4,236,224 entitled "Low Roundoff Noise Digital Filter" issued to T. L. Chang describes recursive filters wherein the sample sums from the combining means are truncated by dropping a number of least significant bits. The effect of truncation is reduced by scaling the dropped or roundoff bits, delaying and subtractively combining the scaled roundoff bits with the incoming signal and the delayed combined signal samples.
The foregoing systems tend to reduce anomalies produced by sample truncation, however, the corrections applied are constrained to the quantization value of the processed samples. In accordance with an aspect of the present invention truncation errors are reduced by introducing correction factors with effective higher resolution than the quantization value of the processed samples.